X-ray diffractometry (XRD) is a well-known technique for studying the crystalline structure of matter. In XRD, a sample is irradiated by a monochromatic X-ray beam, and the locations and intensities of the diffraction peaks are measured. The characteristic diffraction angles and the intensity of the diffracted radiation depend on the lattice planes of the sample under study and the atoms that make up the crystalline material. For a given wavelength λ and lattice plane spacing d, diffraction peaks will be observed when the X-ray beam is incident on a lattice plane at angles θ that satisfy the Bragg condition: nλ=2d sin θB, wherein n is the scattering order. The angle θB, that satisfies the Bragg condition is known as the Bragg angle. Distortions in the lattice planes due to stress, solid solution, or other effects lead to observable changes in the XRD spectrum.
XRD has been used, inter alia, for measuring characteristics of single-crystal layers produced on semiconductor wafers. In some of these measurements, relative angular tilt between the layers is taken into account. For example, Pesek et al. describe XRD techniques of this sort in “Lattice Misfit and Relative Tilt of Lattice Planes in Semiconductor Heterostructures,” Semiconductor Science and Technology 6 (1991), pages 705-708, which is incorporated here by reference. The authors used XRD to investigate the tilt in various compound semiconductor layers grown on miscut GaAs substrates.
Cohen et al. describe similar techniques in “High-Resolution X-Ray Diffraction for Characterization and Monitoring of Silicon-on-Insulator Fabrication Processes,” Journal of Applied Physics 93 (2003), pages 245-250, which is also incorporated herein by reference. The authors found XRD to be applicable to multilayered silicon-on-insulator (SOI) structures fabricated by wafer bonding. The tilt and rotation of each crystalline layer with respect to the substrate allowed them to obtain independent measurements of each SOI film.